Parallel mechanisms show desirable
characteristics such as a large payload to robot weight ratio, considerable
stiffness, low inertia and high dynamic performances. In particular, parallel
manipulators with fewer than six degrees of freedom have recently attracted
researchers' attention, as their employ may prove valuable in those applications
in which a higher mobility is uncalled-for.

The attention of this paper
is focused on translational parallel mechanisms (TPMs), that is on parallel
mechanisms whose output link (platform) is provided with a pure translational
motion with respect to the frame.

It deals with the general
problem of the topological synthesis and classification of TPMs and it investigates
both their constraint and direct singularities. In particular, it identifies
for the first time special families of fully-isotropic mechanisms. Such
manipulators exhibit outstanding properties, as they are free from singularities
and show a constant orthogonal Jacobian matrix throughout their workspace.
As a consequence, both the direct and the inverse position problems are
linear and the kinematic analysis proves straightforward.